Research on fusing topological data analysis with convolutional neural network

Abstract: Convolutional Neural Network (CNN) struggle to capture the multi-dimensional structural information of complex high-dimensional data, which limits their feature learning capability. This paper proposes a feature fusion method based on Topological Data Analysis (TDA) and CNN, named TDA-CNN. This method combines numerical distribution features captured by CNN with topological structure features captured by TDA to improve the feature learning and representation ability of CNN. TDA-CNN divides feature extraction into a CNN channel and a TDA channel. CNN channel extracts numerical distribution features, and the TDA channel extracts topological structure features. The two types of features are fused to form a combined feature representation, with the importance weights of each feature adaptively learned through an attention mechanism. Experimental validation on datasets such as Intel Image, Gender Images, and Chinese Calligraphy Styles by Calligraphers demonstrates that TDA-CNN improves the performance of VGG16, DenseNet121, and GoogleNet networks by 17.5%, 7.11%, and 4.45%, respectively. TDA-CNN demonstrates improved feature clustering and the ability to recognize important features. This effectively enhances the model's decision-making ability.